Question

A metallic right circular cone 20 cm high and whose vertical angle is 90 degree is cut into two parts at the middle of its height by a plane parallel to its base. The structure so obtained be drawn into a wire of diameter 1/16cm,find the length of the wire and Total surface area of structure....

Answer 1

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BEFORE THE ATTACHMENT:-

Let ABC be the metallic cone
AO = 20 cm
cone is cut into two parts at the middle
hence height of the frustum
AD = 10 cm
since A is right angle
So each angle B & C = 45°
And E & F = 45°

Let radii of top and bottom circles of frustum be r1 and r2

in ADE
DE/AD = cot 45°
r1 /10 = 1
r1 = 10

in AOB
OB / OA = cot 45°
r2 /20 = 1
r2 = 20
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AFTER THE ATTACHMENT:-
therefore volume of the metal used in the wire = volume of frustum

pi l/ 1024 = 7000 pi / 3
l = (7000 x 1024)/ 3
l= 2389333.33 cm
l= 23893.33 m

therefore length of the wire = 23893.33m

Answer 2

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